Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 6x + 2$ and $ BC = 5x + 3$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {6x + 2} = {5x + 3}$ Solve for $x$ $ x = 1$ Substitute $1$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 6({1}) + 2$ $ BC = 5({1}) + 3$ $ AB = 6 + 2$ $ BC = 5 + 3$ $ AB = 8$ $ BC = 8$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {8} + {8}$ $ AC = 16$